The desire to test private members is a design smell, generally indicating that there is a class trapped inside your class struggling to get out. All of the functionality of a class should be exercisable through its public methods; functionality that can't be accessed publicly doesn't actually exist.
There are a couple of approaches to realizing that you need to test that your private methods do what they say on the tin. Friend classes are the worst of these; they tie the test to the implementation of the class under test in a way that is prima facie fragile. Somewhat better is dependency injection: Making the private methods' dependencies class attributes that the test can supply mocked-up versions of so as to allow the testing of private methods through the public interface. Best is to extract a class that encapsulates the behavior your private methods have as its public interface, and then test the new class as you normally would.
For more details, consult Clean Code.
